Crossword-Solution: CONFORMAL 9 letters, 2 clues 🏆 scrabble score: 16

Conformal Representation in General._--Consider a circle of radius a lying within the region of existence of a single valued monogenic function, u + iv, of the complex variable z, = x + iy, the origin z = 0 being the centre of this circle.

This being assumed, we obtain a conformal representation of the interior of the region R upon the interior of a circle, in which the arbitrary interior point c of R corresponds to the centre of the circle, and, by utilizing the arbitrary constant arising in determining the function Q, an arbitrary point of the boundary of R corresponds to an arbitrary point of the circumference of the circle.

There is thus a conformal representation of the interior of the slit semicircle in the z-plane, upon the interior of the whole semicircle in the [zeta]-plane, the function z = [([zeta]² - h²) / (1 - h²[zeta]²)]^½ being single valued in the latter semicircle.

Such surfaces are capable of a conformal representation on a plane, by which geodesics are represented by straight lines.